dorsal/arxiv
View SchemaQuelques applications de l'Ansatz de Bethe (Some applications of the Bethe Ansatz)
| Authors | P. Zinn-Justin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9810007 |
| URL | https://arxiv.org/abs/solv-int/9810007 |
Abstract
The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex models) and relativistic field theories with 1 space dimension and 1 time dimension. The connection with quantum groups is expounded. Several applications are then presented. Finite size corrections are calculated via two methods: The Non-Linear Integral Equations, which are applied to the study of the states of the affine Toda model with imaginary coupling, and their interpolation between the high energy (ultra-violet) and low energy (infra-red) regions; and the Thermodynamic Bethe Ansatz Equations, along with the associated Fusion Equations, which are used to determine the thermodynamic properties of the generalized multi-channel Kondo model. The latter is then studied in more detail, still using the Bethe Ansatz and quantum groups, so as to characterize the spectrum of the low energy excitations.
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"abstract": "The Bethe Ansatz is a method that is used in quantum integrable models in\norder to solve them explicitly. This method is explained here in a general\nframework, which applies to 1D quantum spin chains, 2D statistical lattice\nmodels (vertex models) and relativistic field theories with 1 space dimension\nand 1 time dimension. The connection with quantum groups is expounded. Several\napplications are then presented. Finite size corrections are calculated via two\nmethods: The Non-Linear Integral Equations, which are applied to the study of\nthe states of the affine Toda model with imaginary coupling, and their\ninterpolation between the high energy (ultra-violet) and low energy (infra-red)\nregions; and the Thermodynamic Bethe Ansatz Equations, along with the\nassociated Fusion Equations, which are used to determine the thermodynamic\nproperties of the generalized multi-channel Kondo model. The latter is then\nstudied in more detail, still using the Bethe Ansatz and quantum groups, so as\nto characterize the spectrum of the low energy excitations.",
"arxiv_id": "solv-int/9810007",
"authors": [
"P. Zinn-Justin"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Quelques applications de l\u0027Ansatz de Bethe (Some applications of the Bethe Ansatz)",
"url": "https://arxiv.org/abs/solv-int/9810007"
},
"schema_id": "dorsal/arxiv",
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"type": "Model",
"variant": "snapshot-2026-03-01",
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